Model-Theoretic Algebra With particular emphasis on fields, rings, modules

M. Prest
1993 Bulletin of the London Mathematical Society  
BOOK REVIEWS 195 been omitted from an introductory text; the Lachlan-Kotlarski-Krajewski results on satisfaction classes are certainly difficult, but they have hitherto played a marginal role in the mainstream development of the field. On the other hand, I feel that the author missed an opportunity by not including any account of the development in the last ten years of connections between weak arithmetic and computational complexity, a development to which he himself has made a significant
more » ... ribution. These connections have intellectually fascinating implications. The book is well supplied with instructive exercises, and a final chapter details suggestions for further reading, including references to the development just mentioned. There is a well chosen, but not exhaustive, bibliography. As a whole, this book is highly recommended for the serious student of models of arithmetic. Edited by ALI NESIN and ANAND PILLAY: 209 pp., £13.95, ISBN 0 268 01371 3 (University of Notre Dame Press, 1989). GROUPES STABLES By BRUNO POIZAT: 215 pp., FF.100.00, ISBN 2 9500 9191 1 (Nur al-Mantiq wal-Ma'rifah, 1987).
doi:10.1112/blms/25.2.195 fatcat:pnriywskevbfxmguff6z3dewky